A researcher investigates whether there is correlation between the logarithm of bacterial count and time. For a random sample of 12 readings, the regression line of log10N\log_{10}Nlog10N on t t\,t is log10N=0.083t+2.14\log_{10}N=0.083t+2.14log10N=0.083t+2.14.
Write the corresponding model N=abtN=ab^tN=abt, giving a a\,a and b b\,b to 3 significant figures.
A two-tailed test of correlation gives r=0.781r=0.781r=0.781 and critical values ±0.7079 \pm0.7079\,±0.7079 at the 1% level. Carry out the test.
State one limitation of using the model for times far beyond those observed.
308 exam-style questions on WJEC A Level Maths 4.3 Statistical hypothesis testing (A-level only), covering 4.3.1 Statistical hypothesis testing (A-level only) and 4.3.2 Statistical hypothesis testing (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.